Darvish came in with an Angel Stadium ERA of 2.10, lowest among active pitchers. He struck out nine, walked one and allowed seven hits in 6 1/3 innings. He's 5-1 with a 2.43 ERA in six Anaheim starts after allowing three earned runs. Erick Aybar and Albert Pujols homered in the Angels' first off Darvish (2-1), who settled down as the Rangers' lead grew early.
Skaggs (2-1) lasted just 2 2/3 innings, allowing six earned runs on eight hits and two unintentional walks. He struck out two.
"They just hit the pitches I was throwing," Skaggs (2-1) said. "They made adjustments and had a good game plan.
"I started OK but then I started falling behind. It's easier to hit when it's 3-1 and 2-0. I wasn't throwing the stikes I want to throw. They got infield hits, one off my glove, one off my foot. You've got to kind of erase this and put it behind you."
Angels manager Mike Scioscia had to nearly empty his bullpen because of Skaggs' quick ouster, saving only back-end specialists Ernesto Frieri and Joe Smith.
Scioscia said the Angels are contemplating a roster move to bring in a fresh arm before the Yankees series that starts Monday.
"The two-seamer, the angle he [Skaggs] had when he was going well, it didn't appear ... at times maybe but not consistently," Scioscia said of his starter. "He's been pitching very well for us. He'll be better next time. He'll reload."
The Angels got a scare in the fifth when an up-and-in Darvish pitch, a 91-mph two-seamer, struck Pujols a glancing blow on the helmet, but he was able to quickly take his base and stay in the game.
"When you hear a ball hit the helmet, you're always concerned, but Albert's fine," Scioscia said.
"I had two strikes on him," Darvish said. "It was a waste pitch. Unfortunately it hit him in the helmet."
In the sixth, the Rangers' Alex Rios bristled and appeared to have some angry words when Angels reliever Michael Kohn threw a pitch inside but down, although nothing else developed from it.
"I don't think he was trying to hit Pujols intentionally," said Rios, who also glared into the Angels' dugout after he hit a bases-loaded triple in the Rangers' five-run ninth off Nick Maronde. "For him [Kohn] to come out and throw intentionally at me was not right. It is what it is, but it's not right."
Kohn said he didn't hear Rios, and added he wasn't trying to hit him.
"Michael Kohn was trying to pitch aggressively inside, like Darvish was," Sciosicia said. "That's part of the game."
Darvish had allowed just two home runs in five previous starts in Anaheim. The Angels matched that in the bottom of the first. Aybar hit a 3-2 fastball out to right-center and, a batter later, Pujols hit career homer No. 502 into the rockpile in straightaway center field on a 96-mph Darvish fastball.
A potential big second inning for the Angels was short-circuited when Rangers manager Ron Washington successfully challenged umpire Lance Barrett's safe call on an attempted force play at third base, taking an infield hit away from Aybar. He had to settle for three hits, a triple shy of the cycle. The review showed Rangers third baseman Adrian Beltre stayed on the bag to take Darvish's throw and force out C.J. Cron (who had two more hits for a two-game total of five in his MLB debut).